A random telegraph signal (RTS) is a signal which is observed, in a submicron MOS device, a Josephson device, a SQUID, a two-dimensional electron gas, a quantum dot, etc., as discrete values of physical quantities such as current and voltage, or as low-frequency noise which moves back and forth between levels. It should be noted that binary states have been mainly used for the discrete physical quantities observed in such a signal, and hence studies have been made mainly for the case of the binary states.
The existence of the RTS has been known since a long time ago (since the 1980s), but because of its relatively small power with respect to the main signal, the RTS has rarely been perceived as a problem in terms of operating a device. However, in recent years, due to the fact that devices have become smaller in size, requiring smaller actuating signals, the problems caused by the RTS are beginning to become actual.
For example, in Leyris, C.; Martinez, F.; Valenza, M.; Hoffmann, A.; Vildeuil, J. C.; Roy, F.; “Impact of Random Telegraph Signal in CMOS Image Sensors for Low-Light Levels”; Solid-State Circuits Conference, 2006; ESSCIRC 2006; Proceedings of the 32nd European Sept. 2006; pp.376-379, it is reported that the RTS causes degradation in image quality in a high-resolution CMOS image sensor, that is, an image sensor in which transistors forming pixels are small in size. Apart from the image sensor, microdevices having process sizes of 45 nm or smaller are said to have a risk of increased jitter or, at worst, malfunctions, due to the influence of the RTS. Accordingly, it is believed that the need to develop technology for suppressing the occurrence of the RTS or technology for avoiding the influence thereof has become urgent.
Meanwhile, there are various theories on the cause of the RTS, and there has been no consensus attained so far. According to the most widely accepted theory, for example, in a case of a MOS transistor, the RTS results related to an electron or hole trap caused by a crystal defect in the vicinity of the interface between the semiconductor and the insulating film, that is, oxide film, or within the insulating film. The RTS is consistent with the Poisson distribution (p(t)=(exp(−t/τ))/τ), and the frequency spectrum thereof exhibits a Lorentzian distribution having a gradient of 1/f2. Specific parameters or time constants, that is, coefficients τ can be obtained using a gradient obtained through logarithmic plotting of the frequency or a histogram. It is believed that identifying the energy level or the distance from the interface of a trap causing the RTS would be of great use in studying the mechanism of RTS occurrence and the method of reducing traps. The energy level of a trap can be obtained using Arrhenius plots of the parameters or the time constants, that is, the coefficients τ, which are dependent on the time lengths during which the RTS stays at the two levels. The distance from the interface can be obtained by the ratio between the coefficients τ at the two levels. There is a possibility that further information can be obtained through detailed analyses of the parameters in the future.
For example, as illustrated in FIG. 10, when it is easy, from the observed waveform, to discriminate between the two levels exhibited in the RTS, in the same manner as for a normal binary digital signal, one threshold, that is, a threshold level TH1 is set, whereby the coefficient τ can be easily obtained based on the duration of each of the two levels. However, as illustrated in FIG. 11, when such an RTS containing various noise as is observed in a microfabricated device is observed, it is difficult, with the discrimination method using a single threshold level TH1 according to the conventional method, to appropriately discriminate between the two levels exhibited in the RTS, resulting in difficulties in the analysis.
Meanwhile, in recent years, the reduction of the development period for a semiconductor process or device has been demanded, and hence it has become necessary to perform the RTS analysis for a large amount of devices produced under a variety of manufacturing conditions. Accordingly, it is required that the parameter extraction for the RTS be performed efficiently and at high speed.
It should be noted that the analysis method for a random telegraph signal which contains noise is discussed in Y. Yuzhelevski, M. Yuzhelevski, and G. Jung, “Random telegraph noise analysis in time domain”, Rev. Sci. Instrum. 71, p.1681 (2000), but as indicated by U*up, U*dn of FIG. 5, due to the fact that a threshold which does not change in level across the entire section is conceived, the application to the analysis of an RTS containing large noise as illustrated in FIG. 11 is impossible.